A003104 Number of hexagonal n-element polyominoes whose graph is a path.

1, 1, 2, 4, 10, 24, 67, 182, 520, 1474, 4248, 12196, 35168, 101226, 291565, 838764, 2412033, 6929754, 19896915, 57084939, 163677686, 469008353, 1343165478, 3844533186, 10998790991, 31451726513, 89899650912, 256859865260, 733620238080, 2094559523979, 5978195451960

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

In other words, number of 2-sided strip polyhexes with n cells.

References

• E. M. Palmer, Variations of the cell growth problem, Lect. Notes Math. 303 (1972), 215-224.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• N. Trinajstić, S. Nikolić, J. V. Knop, W. R. Müller and K. Szymanski, Computational Chemical Graph Theory: Characterization, Enumeration, and Generation of Chemical Structures by Computer Methods, Ellis Horwood, 1991.

Links

• A. T. Balaban, J. Brunvoll, B. N. Cyvin & S. J. Cyvin, Enumeration of branched catacondensed benzenoid hydrocarbons and their numbers of Kekulé structures Tetrahedron, 44(1) (1988), 221-228. See Table 1.
• Wenchen He and Wenjie He, Generation and enumeration of planar polycyclic aromatic hydrocarbons, Tetrahedron 42.19 (1986): 5291-5299. See Table 1, column B.
• Ed Pegg, Jr., Illustrations of polyforms
• Eric Weisstein's World of Mathematics, Polyhex

Crossrefs

Cf. A323931, A323932.

Extensions

a(8)-a(12) from Ed Pegg Jr, May 13 2009

a(13)-a(19) from Joseph Myers, Nov 26 2010

a(20) from Trinajstić et al. (Table 4.2, the number of cata-condensed benzenoids with h hexagons, unbranched) added by Andrey Zabolotskiy, Feb 08 2023

a(21)-a(31) from Bert Dobbelaere, May 07 2025